5.4 Vocabulary legs of an isosceles triangle vertex angle base base angles
Recall that an isosceles triangle has at least two congruent sides Recall that an isosceles triangle has at least two congruent sides. The congruent sides are called the legs. The vertex angle is the angle formed by the legs. The side opposite the vertex angle is called the base, and the base angles are the two angles that have the base as a side. 3 is the vertex angle. 1 and 2 are the base angles. Remember Definition of isosceles triangle: If isos then at least 2 congruent sides (converse?)
Isosceles Triangle Base Angles Theorem 5-6 5-7 Inverse and Countrapositive???
Two Related Theorems from Ch 6: The positions of the longest and shortest sides of a triangle correspond to the positions of the largest and smallest angles. 6-9 6-10
Example 1: Astronomy Application The length of YX is 20 feet. Explain why the length of YZ is the same.
Example 2A: Finding the Measure of an Angle Find mF. Example 2B: Finding the Measure of an Angle Find mG.
The following corollary and its converse show the connection between equilateral triangles and equiangular triangles. 5-2 5-3
Example 3A: Using Properties Find the value of x. Example 3B: Find the value of y.
Example 4A: For isosceles ∆LMP with LM the base, MP = 2x + 10, PL = x + 30, LM = 4x. Find MP Example 4B: ∆OLD is isosceles with base OL, O= 3x, L = 2x + 15, D = 4x + 30, LM = 4x. Find each angle.
Lesson Quiz: Part I Find each angle measure. 1. mR 2. mP Find each value. 3. x 4. y 5. x
Lesson Quiz: Part II 6. The vertex angle of an isosceles triangle measures (a + 15)°, and one of the base angles measures 7a°. Find a and each angle measure. Classifying triangles by angles and sides: Slide with angle-side problems In triangle ABC BC<CA<AB. List the angles from smallest to largest.